{
"cells": [
{
"cell_type": "markdown",
"id": "5b03aa44",
"metadata": {},
"source": [
"# Cálculo de autovalores\n",
"#### https://meet.noysi.com/metodosnumericos1"
]
},
{
"cell_type": "markdown",
"id": "45aa23c7-93ab-4aa9-9d99-034f3b5b622d",
"metadata": {},
"source": [
"## Teorema de Gersgorin"
]
},
{
"cell_type": "markdown",
"id": "8b0f9d74-f584-45e7-bbdc-1caf53f0ff41",
"metadata": {},
"source": [
"La siguientes funciones calculan los discos del Teorema de Gersgorin y los representan."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "a502845e-5ac5-4221-9f93-3f24dc372fb7",
"metadata": {},
"outputs": [],
"source": [
"def Gershgorin(A):\n",
" return zip(A.diagonal(),vector([sum([abs(k) for k in fila]) for fila in A])-vector(map(abs,A.diagonal())) )\n",
"def discosG(A):\n",
" B=matrix(CDF,A)\n",
" cr=Gershgorin(B)\n",
" discos= sum([ circle([c.real(),c.imag()],r,fill=true,alpha=0.2) for c,r in cr])\n",
" return discos"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "85ac3292",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrr}\n",
"4 & -1 & 1 \\\\\n",
"-1 & -3 & 1 \\\\\n",
"1 & 2 & 5\n",
"\\end{array}\\right) \\left[-3.426743094681910?, 3.757942566075653?, 5.668800528606257?\\right]$$"
],
"text/plain": [
"[ 4 -1 1]\n",
"[-1 -3 1]\n",
"[ 1 2 5] [-3.426743094681910?, 3.757942566075653?, 5.668800528606257?]"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": "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\n",
"text/plain": [
"Graphics object consisting of 3 graphics primitives"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"A = matrix([[4,-1,1],[-1,-3,1],[1,2,5]])\n",
"show(A,A.eigenvalues())\n",
"discosG(A)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "f36b686f-e381-470e-bb94-d0554908757c",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"id": "d712e005-e37e-4890-bf70-34fbe810b8f0",
"metadata": {},
"source": [
"\n",
" Ejercicio 1. \n",
"\n",
"a) Aplicar el Teorema de Gersgorin para localizar los autovalores de la matriz \n",
"$$A=\\left(\\begin{array}{rrr} 15.0 & -1.0 & 1.0 \\\\ 2.0 & -5.0 & 1.0 \\\\ 1.0 & 1.0 & -3.0 \\end{array}\\right). $$\n",
"\n",
"b) Aplicar el método de la potencia para aproximar el autovalor de módulo máximo. En cada paso, normaliza el vector. Detener el método cuando $\\|A v_k - \\lambda_k v_k\\|_2<10^{-2}$, donde $\\lambda_k$ es el autovalor aproximado obtenido y $v_k$ es el vector normalizado correspondiente a dicha iteración (que es una aproximación del autovalor). Aplicar el método con varios pasos y representar los valores obtenidos para $\\|A v_k - \\lambda_k v_k\\|_2<10^{-2}$. \n",
" \n",
"c) Aplicar el método de la potencia para aproximar el autovalor de módulo máximo, pero tomando como vector inicial uno de los autovectores correspondientes a un autovalor que no sea el de módulo máximo. Realizar $100$ iteraciones del método y representar el error residual $\\|A v_k - \\lambda_k v_k\\|_2$. \n",
"\n",
"d) Aplicar el método de la potencia inversa para aproximar el autovalor de módulo mínimo, con las mismas consideraciones que en el apartado b).\n",
"\n",
"e) Aplicar el método de la potencia inversa desplazada para encontrar el autovalor restante, con las mismas consideraciones que en el apartado b).\n",
" \n",
"
"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "b2b95a04",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/latex": [
"$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrr}\n",
"15.0 & -1.0 & 1.0 \\\\\n",
"2.0 & -5.0 & 1.0 \\\\\n",
"1.0 & 1.0 & -3.0\n",
"\\end{array}\\right) \\left[14.958148652677082, -2.639723010334766, -5.318425642342307\\right]$$"
],
"text/plain": [
"[15.0 -1.0 1.0]\n",
"[ 2.0 -5.0 1.0]\n",
"[ 1.0 1.0 -3.0] [14.958148652677082, -2.639723010334766, -5.318425642342307]"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": "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\n",
"text/plain": [
"Graphics object consisting of 3 graphics primitives"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"A = matrix(CDF,[[15,-1,1],[2,-5,1],[1,1,-3]])\n",
"show(A,A.eigenvalues())\n",
"discosG(A)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "4bc4d1ef",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(1.0, 1.0, 1.0)"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"v0 = vector(CDF,[1,1,1])\n",
"v0"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "f7b23954",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(4.0, 11.452168961076477)"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"v1 = A*v0\n",
"l1 = v0.conjugate()*v1/(v0.conjugate()*v0)\n",
"v1 = v1.normalized()\n",
"l1, (A*v1-l1*v1).norm(2)"
]
},
{
"cell_type": "code",
"execution_count": 22,
"id": "a5af60b1",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(14.330434782608696, 1.3641109299063303)"
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"v2 = A*v1\n",
"l2 = v1.conjugate()*v2/(v1.conjugate()*v1)\n",
"v2 = v2.normalized()\n",
"l2, (A*v2-l2*v2).norm(2)"
]
},
{
"cell_type": "code",
"execution_count": 23,
"id": "94fe814e",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(14.664465593249199, 0.5678578314868246)"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"v3 = A*v2\n",
"l3 = v2.conjugate()*v3/(v2.conjugate()*v2)\n",
"v3 = v3.normalized()\n",
"l3, (A*v3-l3*v3).norm(2)"
]
},
{
"cell_type": "code",
"execution_count": 33,
"id": "27cbac74",
"metadata": {},
"outputs": [],
"source": [
"v0 = vector(CDF,[1,1,1])\n",
"err = []\n",
"for _ in range(10):\n",
" v1 = A*v0\n",
" l1 = v0.conjugate()*v1/(v0.conjugate()*v0) # Rayleigh\n",
" v1 = v1.normalized()\n",
" err.append( (A*v1-l1*v1).norm(2) )\n",
" v0 = copy(v1)"
]
},
{
"cell_type": "code",
"execution_count": 30,
"id": "b038ae2f",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAnQAAAHUCAYAAACznbW8AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjYuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/P9b71AAAACXBIWXMAAA9hAAAPYQGoP6dpAAAqcklEQVR4nO3dfXBV9Z3H8c9NMOEp9yLU8BggYITcnKugXEvVsbpad5S6tna1a+3WxX3oQ0QoMy2y1nZ9gIyu67o73uLgdFtahsp2W1xG11bHtuCzID6kCRCe5MGCUMV7woOBJGf/OE1IIJCnc+7vnHPfr5k719zc3PMNaWfec875nRNzHMcRAAAAQqvA9AAAAADoH4IOAAAg5Ag6AACAkCPoAAAAQo6gAwAACDmCDgAAIOQIOgAAgJALXNA5jiPbtsXl8QAAAHomcEHX2NioRCKhxsZG06MAAACEQuCCDgAAAL1D0AEAAIQcQQcAABByBB0AAEDIEXQAAAAhR9ABAACEXGCCLpPJKJlMasaMmZKk5mbDAwEAAIREzAnYFXyffdbWddcl9PrrWV18cdz0OAAAAIEXmD10bSor3ef6erNzAAAAhEXggm74cPeZoAMAAOiZwAVdG4IOAACgZwIbdBs3mp4AAAAgHAIbdNu3S0eOmJ4CAAAg+AIbdBJ76QAAAHoi0EH3hz+YngAAACD4Aht0EycSdAAAAD0R2KCrrCToAAAAeiKwQZdMEnQAAAA9Edigq6yU9uyRDh40PQkAAECwBTbokkn3ua7O7BwAAABBF9igq6iQBgzgsCsAAEB3Aht0RUXSeecRdAAAAN0JbNBJUipF0AEAAHQn0EFnWW7QOY7pSQAAAIIrMEGXyWSUTCaVTqfbX7Ms6cMPpQ8+MDgYAABAwMUcJ1j7v2zbViKRUDab1f79cVVUSM8/L119tenJAAAAgikwe+i6Ul4uDRrEeXQAAABnEuigKyx0r0dXW2t6EgAAgOAKdNBJJxZGAAAAoGuhCLq6Oqm11fQkAAAAwRSKoDt8WNq50/QkAAAAwRT4oEul3GcOuwIAAHQt8EE3Zow0bBhBBwAAcDqBD7pYjIURAAAAZxL4oJMIOgAAgDMJTdBt2iQdP256EgAAgOAJTdAdOyZt2WJ6EgAAgOAJRdBVVbnPHHYFAAA4VSiC7lOfkkaNIugAAAC6Eoqgk1gYAQAAcDqhCbpUiqADAADoSmiCzrKkrVulo0dNTwIAABAsgQm6TCajZDKpdDrd5fctS3IcaePGHA8GAAAQcDHHcRzTQ3Rk27YSiYSy2azi8Xj764cOSSUl0rJl0te+ZnBAAACAgAnMHrruDB0qlZdzHh0AAMDJQhN0knvYtbbW9BQAAADBErqgYw8dAABAZ6ELuj17pI8/Nj0JAABAcIQu6CSprs7sHAAAAEESqqCbOlUaMIDDrgAAAB2FKuiKiqTzziPoAAAAOgpV0EksjAAAADhZKIOutta9awQAAABCGnQffijt3296EgAAgGAIZdBJXGAYAACgTeiCbtIkaeBAzqMDAABoE7qgKyyUkkmCDgAAoE2vg27t2rW6/vrrNWbMGMViMT311FOdvu84jv7lX/5FY8aM0aBBg3TFFVeozuMrAbPSFQAA4IReB93hw4d1wQUX6LHHHuvy+w899JAeeeQRPfbYY1q3bp1GjRqlz33uc2psbOz3sG1SKfduEa2tnn0kAABAaA3o7Q9ce+21uvbaa7v8nuM4evTRR3X33XfrxhtvlCQtW7ZMI0eO1IoVK/T1r3/9lJ9pampSU1NT+9e2bXc7g2VJhw5Ju3ZJEyf29jcAAACIFk/PoduxY4f27duna665pv214uJiffazn9Urr7zS5c/U1NQokUi0P8rKyrrdTttKVw67AgAAeBx0+/btkySNHDmy0+sjR45s/97JFi5cqGw22/7YvXt3t9sZO1ZKJAg6AAAAqQ+HXHsiFot1+tpxnFNea1NcXKzi4uJefj4LIwAAANp4uodu1KhRknTK3rj9+/efsteuv9puAQYAAJDvPA268vJyjRo1Ss8//3z7a8eOHdOaNWt0ySWXeLkpWZa0aZN0/LinHwsAABA6vT7keujQIW3durX96x07dujtt9/W8OHDNX78eM2bN0+LFy9WRUWFKioqtHjxYg0ePFhf+cpXPB3csqRjx6StW6XKSk8/GgAAIFR6HXTr16/XlVde2f71/PnzJUm33XabfvKTn+i73/2ujh49qm9961s6ePCgPv3pT+u5555TSUmJd1Or80pXgg4AAOSzmOM4jukhOrJtW4lEQtlsVvF4/IzvHT1a+qd/ku69N0fDAQAABFDo7uXaEStdAQAACDoAAIDQC33Qbd0qHT1qehIAAABzQh90ra3u5UsAAADyVaiDLpl0n7nAMAAAyGehDrqSEmniRM6jAwAA+S3UQSexMAIAAICgAwAACLnQB10qJe3eLWWzpicBAAAwI/RB13YLsLo6s3MAAACYEvqgmzJFKizksCsAAMhfgQm6TCajZDKpdDrdq58rLpbOO4+gAwAA+SvmOI5jeoiObNtWIpFQNptVPB7v0c/cfLN04ID0u9/5PBwAAEAABWYPXX9Ylntx4WClKQAAQG5EJug+/FDav9/0JAAAALkXmaCTOI8OAADkp0gE3eTJ0sCBBB0AAMhPkQi6wkIpmSToAABAfopE0EncAgwAAOSvyAUdK10BAEC+iVTQHTok7dplehIAAIDcilTQSe716AAAAPJJZIJu3DgpHuc8OgAAkH8iE3SxGAsjAABAfopM0EkEHQAAyE+RCrpUStq4UWpuNj0JAABA7kQq6CxLOnZM2rrV9CQAAAC5E6mgq6pynznsCgAA8kmkgu6cc6SRIwk6AACQXwITdJlMRslkUul0ul+fw8IIAACQb2KOE6ybZdm2rUQioWw2q3g83uufnzdPevZZafNm72cDAAAIosDsofOKZbmLIo4eNT0JAABAbkQy6FpbpU2bTE8CAACQG5ELOla6AgCAfBO5oCspkSZOJOgAAED+iFzQSax0BQAA+YWgAwAACLnIBt2uXZJtm54EAADAf5ENOkmqqzM7BwAAQC5EMuimTJEKC6XaWtOTAAAA+C+SQTdwoFRRwXl0AAAgP0Qy6CQWRgAAgPxB0AEAAIRcZIMulZIOHJD27zc9CQAAgL8iG3RtK13ZSwcAAKIuskE3ebJUXEzQAQCA6Its0BUWSskkQQcAAKIvMEGXyWSUTCaVTqc9+0wWRgAAgHwQcxzHMT1ER7ZtK5FIKJvNKh6P9+uzHnpIeuABKZuVYjGPBgQAAAiYwOyh84NlSY2N7n1dAQAAoiryQSdx2BUAAERbpIOurEyKxwk6AAAQbZEOuliMhREAACD6Ih10EkEHAACiLy+CbuNGqbnZ9CQAAAD+yIuga2qStm0zPQkAAIA/8iLoJA67AgCA6Ip80J1zjlRaKtXWmp4EAADAH5EPOomFEQAAINoIOgAAgJDLm6DbskX65BPTkwAAAHjP86Brbm7W9773PZWXl2vQoEGaNGmS7rvvPrW2tnq9qR5LpaTWVmnTJmMjAAAA+GaA1x/44IMP6vHHH9eyZctUVVWl9evXa/bs2UokEpo7d67Xm+uRZNJ9/sMfpGnTjIwAAADgG8+D7tVXX9UNN9ygWbNmSZImTpyon//851q/fr3Xm+qxeFyaMIHz6AAAQDR5fsj1sssu0wsvvKCGhgZJ0jvvvKOXXnpJ1113XZfvb2pqkm3bnR5+YGEEAACIKs/30C1YsEDZbFZTp05VYWGhWlpatGjRIt1yyy1dvr+mpkb33nuv12OcwrKkJ5/0fTMAAAA55/keupUrV2r58uVasWKFNmzYoGXLlunhhx/WsmXLunz/woULlc1m2x+7d+/2eiRJbtDt3Cn5tAMQAADAmJjjOI6XH1hWVqa77rpL1dXV7a898MADWr58uTb1YJmpbdtKJBLKZrOKx+OezfX229L06dIrr0if+YxnHwsAAGCc53vojhw5ooKCzh9bWFho9LIlkjR1qlRQwHl0AAAgejw/h+7666/XokWLNH78eFVVVemtt97SI488ottvv93rTfXKwIFSRQVBBwAAosfzQ66NjY265557tGrVKu3fv19jxozRLbfcou9///sqKirq9uf9OuQqSTfdJH30kfTCC55+LAAAgFGeB11/+Rl0994r/fCH0gcfePqxAAAARuXFvVzbWJa0f7/7AAAAiIq8CzpJqqszOwcAAICX8iroJk+WiotZGAEAAKIlr4JuwACpslKqrTU9CQAAgHfyKugk7ukKAACiJ2+DLlhrewEAAPouL4OusVHy6ZaxAAAAOZd3QZdKuc8cdgUAAFGRd0FXViaVlBB0AAAgOvIu6GIxFkYAAIBoybugkwg6AAAQLYEJukwmo2QyqXQ67fu2LEuqr5daWnzfFAAAgO9ijhOsC3jYtq1EIqFsNqt4PO7LNn77W+mqq6RNm6QpU3zZBAAAQM4EZg9dLrXd05XDrgAAIAryMuhKS6VzziHoAABANORl0EksjAAAANGRt0GXShF0AAAgGvI26CxL2rJF+uQT05MAAAD0T14HXUuLtHmz6UkAAAD6J2+DrqrKfeawKwAACLu8Dbp4XBo/nqADAADhl7dBJ7mHXWtrTU8BAADQP3kfdOyhAwAAYZf3Qbdzp2TbpicBAADou7wPOkmqrzc7BwAAQH/kddBVVkoFBRx2BQAA4ZbXQTdwoFRRQdABAIBwy+ugk1gYAQAAwo+gI+gAAEDIEXSW9MEH0oEDpicBAADom8AEXSaTUTKZVDqdzul221a6spcOAACEVcxxHMf0EB3Ztq1EIqFsNqt4PO779pqbpSFDpIcflubM8X1zAAAAngvMHjpTBgxwL1/CHjoAABBWeR90EgsjAABAuBF0klIpN+iCdfAZAACgZwg6uXvobFvas8f0JAAAAL1H0ImVrgAAINwIOknjx0tDhxJ0AAAgnAg6SbGYu5euttb0JAAAAL1H0P0ZK10BAEBYEXR/ZllSfb3U0mJ6EgAAgN4h6P7MsqSmJmnbNtOTAAAA9A5B92eplPvMYVcAABA2BN2flZZK55xD0AEAgPAh6DpgYQQAAAgjgq4Dgg4AAIQRQdeBZUkNDe7iCAAAgLAg6DqwLPeyJZs2mZ4EAACg5wITdJlMRslkUul02tgMVVXuM4ddAQBAmMQcx3FMD9GRbdtKJBLKZrOKx+M53/748dKtt0o1NTnfNAAAQJ8EZg9dULAwAgAAhA1Bd5JUiqADAADhQtCdxLKk996TGhtNTwIAANAzBN1JLMt9rq83OwcAAEBPEXQnmTpVKijgsCsAAAgPgu4kgwZJ555L0AEAgPAg6LpgWVJtrekpAAAAeoag6wKXLgEAAGFC0HXBsqQPPpAOHDA9CQAAQPcIui60rXStqzM7BwAAQE8QdF2oqJCKijjsCgAAwoGg68KAAVJlJUEHAADCwZege//99/XVr35VI0aM0ODBgzVt2jS9+eabfmzKNyyMAAAAYTHA6w88ePCgLr30Ul155ZV69tlnVVpaqm3btmnYsGFeb8pXliU9/bTkOFIsZnoaAACA0/M86B588EGVlZXpxz/+cftrEydO9HozvrMsKZuV3n9fGjfO9DQAAACn5/kh19WrV2vGjBm66aabVFpaqunTp+uJJ5447fubmppk23anRxC0rXTlAsMAACDoPA+67du3a8mSJaqoqNBvfvMbfeMb39Cdd96pn/70p12+v6amRolEov1RVlbm9Uh9Mn68NHQo59EBAIDgizmO43j5gUVFRZoxY4ZeeeWV9tfuvPNOrVu3Tq+++uop729qalJTU1P717Ztq6ysTNlsVvF43MvRem3mTGnKFGnZMqNjAAAAnJHne+hGjx6tZDLZ6bXKykrt2rWry/cXFxcrHo93egQFK10BAEAYeB50l156qTZv3tzptYaGBk2YMMHrTfkulZLq66WWFtOTAAAAnJ7nQfftb39br732mhYvXqytW7dqxYoVWrp0qaqrq73elO8sS/rkE2n7dtOTAAAAnJ7nQZdOp7Vq1Sr9/Oc/l2VZuv/++/Xoo4/q1ltv9XpTvmtb6cphVwAAEGSeL4roL9u2lUgkArEownGk0lLpzjule+4xOgoAAMBpcS/XM4jFWBgBAACCj6DrhmVxcWEAABBsBF03LEtqaJA6XCoPAAAgUAi6bliWe9mSk67EAgAAEBgEXTeqqtxnzqMDAABBRdB1Y9gwqayMoAMAAMFF0PUAK10BAECQEXQ9QNABAIAgI+h6wLKkHTukQ4dMTwIAAHAqgq4H2m4BVl9vdg4AAICuEHQ9UFnp3jWCCwwDAIAgCkzQZTIZJZNJpdNp06OcYtAg6dxzOY8OAAAEU8xxHMf0EB3Ztq1EIqFsNqt4PG56nHY33ig1NkrPP296EgAAgM4Cs4cu6FjpCgAAgoqg66FUStq3T/rTn0xPAgAA0BlB10NtK13r6szOAQAAcDKCrofOPVcqKuKwKwAACB6CrofOOkuaOpWgAwAAwUPQ9QILIwAAQBARdL1gWe7FhYN1oRcAAJDvCLpesCwpm5Xef9/0JAAAACcQdL3QttKVw64AACBICLpemDBBGjKEoAMAAMFC0PVCQQELIwAAQPAQdL1E0AEAgKAh6HrJsqT6eqmlxfQkAAAALoKulyxLOnpU2rHD9CQAAAAugq6XWOkKAACChqDrpZEjpREj3AsMAwAABEFggi6TySiZTCqdTpse5YxiMRZGAACAYIk5TrBuZGXbthKJhLLZrOLxuOlxunTHHdLvfifV1ZmeBAAAIEB76MLEsqSGBqmpyfQkAAAABF2fpFJSc7MbdQAAAKYRdH1QVeU+cx4dAAAIAoKuD4YNk8aNI+gAAEAwEHR9xEpXAAAQFARdHxF0AAAgKAi6PrIsaft26dAh05MAAIB8R9D1UdstwOrrzc4BAABA0PVRZaV71wgOuwIAANMIuj4aPFiaPJmgAwAA5hF0/ZBKEXQAAMA8gq4fWOkKAACCgKDrB8uS9u6VPvzQ9CQAACCfEXT90LbSta7O7BwAACC/EXT9UFEhnXWWVFtrehIAAJDPCLp+OOssaepUzqMDAABmEXT9xMIIAABgWmCCLpPJKJlMKp1Omx6lV9qCznFMTwIAAPJVzHGClSK2bSuRSCibzSoej5sep1urV0s33CDt2SONHWt6GgAAkI8Cs4curFIp95nDrgAAwBSCrp8mTJCGDCHoAACAOQRdPxUUSFVVBB0AADCHoPMAK10BAIBJBJ0HLMu9W0RLi+lJAABAPiLoPGBZ0tGj0o4dpicBAAD5iKDzQNs9XTnsCgAATCDoPDBqlDR8OEEHAADMIOg8EIu516Mj6AAAgAkEnUdY6QoAAEwh6DxiWdLmzdKxY6YnAQAA+Yag84hlSc3NUkOD6UkAAEC+8T3oampqFIvFNG/ePL83ZVRVlfvMYVcAAJBrvgbdunXrtHTpUp1//vl+biYQzj5bGjtWqq01PQkAAMg3vgXdoUOHdOutt+qJJ57Q2Wef7ddmAoWFEQAAwATfgq66ulqzZs3S1Vdffcb3NTU1ybbtTo+wIugAAIAJvgTdk08+qQ0bNqimpqbb99bU1CiRSLQ/ysrK/BgpJyxL2r5dOnzY9CQAACCfeB50u3fv1ty5c7V8+XINHDiw2/cvXLhQ2Wy2/bF7926vR8qZVMp9rq83OwcAAMgvMcdxHC8/8KmnntIXv/hFFRYWtr/W0tKiWCymgoICNTU1dfreyWzbViKRUDabVTwe93I03x05Ig0dKv3oR9Ls2aanAQAA+WKA1x941VVXqfakpZ6zZ8/W1KlTtWDBgjPGXNgNHixNnsx5dAAAILc8D7qSkhJZltXptSFDhmjEiBGnvB5FLIwAAAC5xp0iPEbQAQCAXPN8D11Xfv/73+diM4FgWdIf/yh99JE0fLjpaQAAQD5gD53H2o4qs5cOAADkCkHnsYoK6ayzCDoAAJA7BJ3HioqkKVMIOgAAkDsEnQ9SKYIOAADkDkHng7aVrt5eshkAAKBrBJ0PLEs6eFDau9f0JAAAIB8QdD5gpSsAAMglgs4HEye6twEj6AAAQC4QdD4oKJCqqqSTbmkLAADgC4LOJ9wCDAAA5ApB5xPLkurqpNZW05MAAICoC0zQZTIZJZNJpdNp06N4wrKko0elHTtMTwIAAKIu5jjBulqabdtKJBLKZrOKx+Omx+mzvXulMWOkp56SbrjB9DQAACDKArOHLmpGjZKGD+c8OgAA4D+CziexGAsjAABAbhB0PiLoAABALhB0PrIsadMm6dgx05MAAIAoI+h8ZFlSc7PU0GB6EgAAEGUEnY+qqtxnDrsCAAA/EXQ+Gj7cvXQJQQcAAPxE0PmMhREAAMBvBJ3PUimCDgAA+Iug85llSdu3S4cPm54EAABEFUHnM8uSHEfauNH0JAAAIKoIOp9VVrp3jeCwKwAA8AtB57MhQ6RJkwg6AADgH4IuByxLqq01PQUAAIgqgi4HuHQJAADwE0GXA5Yl/fGP0kcfmZ4EAABEUWCCLpPJKJlMKp1Omx7Fc5blPtfVmZ0DAABEU8xxHMf0EB3Ztq1EIqFsNqt4PG56HE8cOyYNHSr9x39I3/ym6WkAAEDUBGYPXZQVFUlTpnAeHQAA8AdBlyMsjAAAAH4h6HKkLeiCdYAbAABEAUGXI5blrnLdt8/0JAAAIGoIuhxpW+nKBYYBAIDXCLocKS+XBg3iPDoAAOA9gi5HCgqkqiqCDgAAeI+gyyFWugIAAD8QdDmUSrl3i2htNT0JAACIEoIuhyxLOnJEeu8905MAAIAoIehyqG2lK4ddAQCAlwi6HBo9Wjr7bIIOAAB4i6DLoViMhREAAMB7BF2OWRYXFwYAAN4i6HLMsqRNm6Rjx0xPAgAAooKgyzHLkpqbpS1bTE8CAACiIjBBl8lklEwmlU6nTY/iK1a6AgAAr8Ucx3FMD9GRbdtKJBLKZrOKx+Omx/HF2LHS7bdL999vehIAABAFgdlDl09Y6QoAALxE0BlA0AEAAC8RdAZYlrRtm3sbMAAAgP4i6AywLMlxpPp605MAAIAoIOgMSCbdZw67AgAALxB0BgwZIk2aRNABAABvEHSGsDACAAB4haAzhKADAABeIegMSaWk99+XDh40PQkAAAg7gs6QtluA1dWZnQMAAIQfQWfIeedJAwZw2BUAAPQfQWdIUZE0ZQpBBwAA+o+gM8iypNpa01MAAICw8zzoampqlE6nVVJSotLSUn3hC1/Q5s2bvd5MJLStdHUc05MAAIAw8zzo1qxZo+rqar322mt6/vnn1dzcrGuuuUaHDx/2elOhZ1nSRx9J+/aZngQAAIRZzHH83T904MABlZaWas2aNbr88su7fb9t20okEspms4rH436OZtzWrVJFhfTcc9LnPmd6GgAAEFa+n0OXzWYlScOHD+/y+01NTbJtu9MjX5SXS4MGsTACAAD0j69B5ziO5s+fr8suu0xW24XXTlJTU6NEItH+KCsr83OkQCkslKqqCDoAANA/vh5yra6u1jPPPKOXXnpJ48aN6/I9TU1Nampqav/atm2VlZXlxSFXSZo9W6qvl15/3fQkAAAgrAb49cFz5szR6tWrtXbt2tPGnCQVFxeruLjYrzECz7KkX/xCam2VCriIDAAA6APPE8JxHN1xxx361a9+pd/+9rcqLy/3ehORYlnS4cPSzp2mJwEAAGHledBVV1dr+fLlWrFihUpKSrRv3z7t27dPR48e9XpTkdB2aiEXGAYAAH3ledAtWbJE2WxWV1xxhUaPHt3+WLlypdebioQxY6Rhw1gYAQAA+s7zc+h8vqxd5MRiJ+4YAQAA0Bechh8ABB0AAOgPgi4ALEvatEk6ftz0JAAAIIwIugBIpdyY27LF9CQAACCMCLoAqKpynznsCgAA+oKgC4ARI6TRowk6AADQNwRdQLAwAgAA9BVBFxCWxcWFAQBA3xB0AWFZ0rZt0pEjpicBAABhQ9AFhGVJjiNt3Gh6EgAAEDYEXUAkk+4z59EBAIDeIugCYuhQadIkgg4AAPReYIIuk8komUwqnU6bHsUYVroCAIC+iDmO45geoiPbtpVIJJTNZhWPx02Pk1N33y399KfS7t2mJwEAAGESmD10cPfQ7dkjffyx6UkAAECYEHQBYlnuc12d2TkAAEC4EHQBMmWKNHCgNHeutGqV1NpqeiIAABAGBF2AFBVJzzwjDR4s3XijVFkpLV0qffKJ6ckAAECQEXQB8xd/Ia1dK736qnsI9hvfkCZMkB54QProI9PTAQCAICLoAmrmTOmXv5Q2bZK++EU36MaPdw/Hvvee6ekAAECQEHQBd9550uOPS7t2SfPnS8uXS+eeK33lK9Jbb5meDgAABAFBFxKlpdJ997lh9+//7h6SvfBC6eqrpeeec+8DCwAA8hNBFzJDhkhz5khbtkhPPikdPCj95V9K06e7e++OHzc9IQAAyDWCLqQGDJC+/GVp/XrphRek0aOlv/1bafJk6ZFHpMZG0xMCAIBcIehCLhZzV8Y++6z0zjvSFVdICxZIZWXSwoXS3r2mJwQAAH4j6CLk/PPde8Fu3y79wz9ImYw0caL0938vbdxoejoAAOAXgi6Cysqkhx92F1Dcf7+79y6ZlP7qr6QXX2QBBQAAUUPQRdiwYdJ3vyvt2CH9139J27ZJl18ufeYz0q9+JbW0mJ4QAAB4gaDLA8XF0uzZUm2t9PTT7tdf+pI0dap7jbujR01PCAAA+oOgyyMFBdKsWdKaNdLrr0vTpknf+pZ7a7H775c+/ND0hAAAoC8CE3SZTEbJZFLpdNr0KHnh4oulX/xCamiQ/vqvpcWL3VuLzZnjHqIFAADhEXOcYJ0ib9u2EomEstms4vG46XHyxoED0mOPuStjDx6UbrpJ+s53pIsuMj0ZAADoTmD20MGsc86R7r3XXRn7n/8prVsnzZjhXuPu179mZSwAAEFG0KGTwYOl6mpp82Zp5Ur3jhPXXitdcIF7jbtjx0xPCAAATkbQoUsDBkg33yy98Yb0u9+517a77TZp0iTp3/5Nsm3TEwIAgDYEHc4oFnNvJ/bMM+5lT66+2r2lWFmZe4uxP/7R9IQAAICgQ49ZlvSTn7irYL/+dfcadhMnSrffLtXXm54OAID8RdCh18aOlR56yF1AsWiR9JvfSFVV0uc/L61dywIKAAByjaBDnyUS7qVNduxw99y995702c9KM2dK//M/3FoMAIBcIejQb0VF7oKJ2lr3XLvBg93r2E2ZIi1Zwq3FAADwG0EHz8Ri0nXXuati33hDuvBC6Y473DtQ3Huv9Kc/mZ4QAIBoIujgi3Ra+u//dm8t9uUvSw8+6IbdHXdI27ebng4AgGgh6OCryZPdW4rt2uVe5mTlSqmiwr3G3bp1pqcDACAaCDrkxKc+Jf3gB9LOnW7gbdggXXyxdOWV0v/9HytjAQDoD4IOOTV4sPTNb7q3FvvFL6QjR6RZs6RUyl0p29RkekIAAMIn5jjB2jdi27YSiYSy2azi8bjpceAzx5FefFH613+Vnn5aGjTIPf/ukkvcx2c+4+7dAwAAp0fQITA2bpR+/WvplVekl1+W9u51X6+oOBF4l1wiJZNSAfuWAQBoR9AhkBzHXUjxyisnHm+/LbW2uhc0njnzROB9+tNSSYnpiQEAMCcwQZfJZJTJZNTS0qKGhgaCDqc4dMhdGdsx8j7+2N1bl0p13otXXu5eFw8AgHwQmKBrwx469FRrq7u4omPgbdrkfm/kyM6Bd+GF0sCBZucFAMAvBB0i5cMPpddeOxF4r7/u3nqsqEi66KLOkTdqlOlpAQDwBkGHSDt+XHr33c578Xbtcr9XXt458FIpqbDQ7LwAAPQFQYe8s2eP9OqrJwJvwwapuVkaOtRdYNEWeDNnSsOGmZ4WAIDuEXTIe0eOSG++2Xkv3p/+5C6qSCY778WrqGCxBQAgeAg64CSOI23d2jnw6urc1z/1Kfdix22BN2OGe/cLAABMIuiAHvj4Y3eBRVvgvfaaexmVAQOk6dM778UbN870tACAfEPQAX3Q0iL94Q+d9+Jt3+5+r6ysc+BdcIF01llm5wUARBtBB3hk377Oiy3Wr5eOHXPvT3vxxZ3vTztihOlpAQBRQtABPmlqclfQtgXeyy9LH3zgfm/KlM578aZO5f60AIC+I+iAHHEc6b33Oh+mffdd944Xw4a5h2ZHjJDOPtv9etiwrv+77XngQFbcAgBcBB1gUGOj9MYbJ1bSfvyx+zh48MTz8eNd/2xRUffxd7r/TiQ4rw8AooSgAwLMcdxbl3WMvN78dzbrfkZXhg49/d6/7v576FAOEQNAkAwwPQCA04vF3OvcDR4sjRnT+59vbXX3AvY0ALdv7/z64cNdf25BgbuXrzd7BTu+NmhQ738XAMDpEXRAhLWFVyLRt58/fvxE8J0uBju+tnt35++f7nBxcXHn4Esk3NeKitxHx//261Fc7B52Zk8jgCgg6ACc1llnSeec4z56qzeHi7NZd1WwbbuXeunpo7m5/7/jgAH+BWNP31tY6IblyY/TvX66R0/ez0IaIJpyEnSO46ixsbHL7zU1Nampqan967b32badi9EA+GzoUPdRVub9Z7e2unsBjx078Xzyo+PrXv23bXe9vTP9bJDEYmeOv1is+1js6j0d33um73f8jJMfbfN58XXH37evP9/de3v7/q6+7vg5J/+devp1d6Hem5/16r29/dkz6el7/fhMP7Y/c6Z7l6GeKikpUaybD8/Jooi2hQ4AAADonZ4sFM1J0PVmD93evXt18cUXq76+XmPHjvV7tC6l02mtW7fOyLZNb9/ktm3bVllZmXbv3m1shXO+/tub3H6+/91Nb5//z+fnv73p7Zv+24ft374ne+hycsg1Fov1+g9WUlJi7P/ghYWFRi+ZYnL7pn93SYrH43n5+5v+tze9/Xz9u5vevunfXcrfv73pf3vT25fM/e1N/+5+bJ/1XV2orq7O2+2b/t1Ny+d/e9PbN8n0757P/7szLZ//7U1v3yTTv7sf2w/chYX37NnTvht23LhxpsdBDnFR6fzE3z1/8bfPX/ztvRe4PXTFxcWdnpE/iouL9YMf/IC/fZ7h756/+NvnL/723gvcHjqqHQAAoHcCt4cOAAAAvUPQAQAAhBxBBwAAEHKBO4eu7SLEPbmIHgAAAAIYdAAAAOgdDrnCuJqaGqXTaZWUlKi0tFRf+MIXtHnzZtNjIcdqamoUi8U0b94806MgB95//3199atf1YgRIzR48GBNmzZNb775pumx4KPm5mZ973vfU3l5uQYNGqRJkybpvvvuU2trq+nRIiEnt/4CzmTNmjWqrq5WOp1Wc3Oz7r77bl1zzTWqr6/XkCFDTI+HHFi3bp2WLl2q888/3/QoyIGDBw/q0ksv1ZVXXqlnn31WpaWl2rZtm4YNG2Z6NPjowQcf1OOPP65ly5apqqpK69ev1+zZs5VIJDR37lzT44Ueh1wROAcOHFBpaanWrFmjyy+/3PQ48NmhQ4d04YUX6oc//KEeeOABTZs2TY8++qjpseCju+66Sy+//LJefPFF06Mghz7/+c9r5MiR+tGPftT+2pe+9CUNHjxYP/vZzwxOFg0cckXgZLNZSdLw4cMNT4JcqK6u1qxZs3T11VebHgU5snr1as2YMUM33XSTSktLNX36dD3xxBOmx4LPLrvsMr3wwgtqaGiQJL3zzjt66aWXdN111xmeLBo45IpAcRxH8+fP12WXXSbLskyPA589+eST2rBhg9atW2d6FOTQ9u3btWTJEs2fP1///M//rDfeeEN33nmniouL9bWvfc30ePDJggULlM1mNXXqVBUWFqqlpUWLFi3SLbfcYnq0SCDoECh33HGH3n33Xb300kumR4HPdu/erblz5+q5557TwIEDTY+DHGptbdWMGTO0ePFiSdL06dNVV1enJUuWEHQRtnLlSi1fvlwrVqxQVVWV3n77bc2bN09jxozRbbfdZnq80CPoEBhz5szR6tWrtXbtWo0bN870OPDZm2++qf379+uiiy5qf62lpUVr167VY489pqamJhUWFhqcEH4ZPXq0kslkp9cqKyv1y1/+0tBEyIXvfOc7uuuuu/Q3f/M3kqRUKqWdO3eqpqaGoPMAQQfjHMfRnDlztGrVKv3+979XeXm56ZGQA1dddZVqa2s7vTZ79mxNnTpVCxYsIOYi7NJLLz3l0kQNDQ2aMGGCoYmQC0eOHFFBQedT9wsLC7lsiUcIOhhXXV2tFStW6H//939VUlKiffv2SZISiYQGDRpkeDr4paSk5JTzJIcMGaIRI0Zw/mTEffvb39Yll1yixYsX6+abb9Ybb7yhpUuXaunSpaZHg4+uv/56LVq0SOPHj1dVVZXeeustPfLII7r99ttNjxYJXLYExp3uFm8//vGP9Xd/93e5HQZGXXHFFVy2JE88/fTTWrhwobZs2aLy8nLNnz9f//iP/2h6LPiosbFR99xzj1atWqX9+/drzJgxuuWWW/T9739fRUVFpscLPYIOAAAg5LgOHQAAQMgRdAAAACFH0AEAAIQcQQcAABByBB0AAEDIEXQAAAAhR9ABAACEHEEHAAAQcgQdAABAyBF0AAAAIUfQAQAAhNz/A/vypupPpQpsAAAAAElFTkSuQmCC\n",
"text/plain": [
"Graphics object consisting of 1 graphics primitive"
]
},
"execution_count": 30,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"list_plot(err,plotjoined=true)"
]
},
{
"cell_type": "code",
"execution_count": 34,
"id": "d7bd8d85",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[(14.958148652677082,\n",
" [(0.9928558625160511, 0.10255006462425884, 0.0609977090804967)],\n",
" 1),\n",
" (-2.639723010334766,\n",
" [(-0.03190857594998693, 0.36686740517079436, 0.9297258465827934)],\n",
" 1),\n",
" (-5.318425642342307,\n",
" [(0.06518858130176128, 0.9057410148550928, -0.41878832705452773)],\n",
" 1)]"
]
},
"execution_count": 34,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"A.eigenvectors_right()"
]
},
{
"cell_type": "code",
"execution_count": 40,
"id": "a832e2c6",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"14.958148652677076"
]
},
"execution_count": 40,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"v0 = vector(CDF,[-0.03190857594998693, 0.36686740517079436, 0.9297258465827934])\n",
"err = []\n",
"aut = []\n",
"for _ in range(50):\n",
" v1 = A*v0\n",
" l1 = v0.conjugate()*v1/(v0.conjugate()*v0) # Rayleigh\n",
" aut.append(l1)\n",
" v1 = v1.normalized()\n",
" err.append( (A*v1-l1*v1).norm(2) )\n",
" v0 = copy(v1)\n",
"l1"
]
},
{
"cell_type": "code",
"execution_count": 46,
"id": "511420c1",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"Graphics object consisting of 2 graphics primitives"
]
},
"execution_count": 46,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"list_plot(err,plotjoined=true) + list_plot(aut,plotjoined=true,color='red')"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "094a1a8e",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"id": "9bcc4693",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"id": "881cd29f",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"id": "996b2806",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"id": "23aba0bd",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"id": "604740fe",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"id": "369e9708",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"id": "c34612fc",
"metadata": {},
"source": [
"\n",
" Ejercicio 2. \n",
"\n",
"a) Utilizar el método de la potencia (desplazando los autovalores si es necesario) para calcular el radio espectral de la matriz\n",
"$$M=\\left(\\begin{array}{rrr} 2.0 & -2.0 & 1.0 \\\\ 3.0 & 2.0 & 1.0 \\\\ 1.0 & 1.0 & -1.0 \\end{array}\\right).$$\n",
"Dibuja en cada paso del método el módulo del error residual $\\|A v_k - \\lambda_k v_k\\|$ obtenido. Detener el método cuando $\\|A v_k - \\lambda v_k\\|_2<10^{-2}$.\n",
" \n",
"b) Calcula el resto de los autovalores.\n",
" \n",
"
"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "b01a43cb",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"id": "4c444e21",
"metadata": {},
"source": [
"\n",
" Ejercicio 3. \n",
" \n",
"a) Aplicar 10 pasos del método QR para aproximar los autovalores de la matriz \n",
"$$\\left(\\begin{array}{rrr} 15.0 & -1.0 & 1.0 \\\\ 2.0 & -5.0 & 1.0 \\\\ 1.0 & 1.0 & -3.0 \\end{array}\\right). $$\n",
"La factorización QR de cada paso, calcularla usando el método `QR` de Sage.\n",
"\n",
"b) Obtener una factorización QR de la matriz anterior, utilizando reflexiones de Householder. \n",
" \n",
"
"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "8a8d48d9",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"id": "fb7ddc10",
"metadata": {},
"source": [
"\n",
" Ejercicio 4. \n",
" \n",
"Encontrar una matriz tal que uno de los discos de Gersgorin no contenga ningún autovalor.\n",
" \n",
"
"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "76231cf2",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "SageMath 9.5",
"language": "sage",
"name": "sagemath"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.11.2"
}
},
"nbformat": 4,
"nbformat_minor": 5
}